man dlaed4 (Fonctions bibliothèques) - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
NAME
DLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
SYNOPSIS
- SUBROUTINE DLAED4(
- N, I, D, Z, DELTA, RHO, DLAM, INFO )
- INTEGER I, INFO, N
- DOUBLE PRECISION DLAM, RHO
- DOUBLE PRECISION D( * ), DELTA( * ), Z( * )
PURPOSE
This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus
diag( D ) + RHO * Z * Z_transpose.
where we assume the Euclidean norm of Z is 1.
The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
ARGUMENTS
- N (input) INTEGER
- The length of all arrays.
- I (input) INTEGER
- The index of the eigenvalue to be computed. 1 <= I <= N.
- D (input) DOUBLE PRECISION array, dimension (N)
- The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J.
- Z (input) DOUBLE PRECISION array, dimension (N)
- The components of the updating vector.
- DELTA (output) DOUBLE PRECISION array, dimension (N)
- If N .ne. 1, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the eigenvectors.
- RHO (input) DOUBLE PRECISION
- The scalar in the symmetric updating formula.
- DLAM (output) DOUBLE PRECISION
- The computed lambda_I, the I-th updated eigenvalue.
- INFO (output) INTEGER
- = 0: successful exit
> 0: if INFO = 1, the updating process failed.
PARAMETERS
Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin.
ORGATI = .true. origin at i ORGATI = .false. origin at i+1
Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles!
MAXIT is the maximum number of iterations allowed for each eigenvalue.
Further Details ===============
Based on contributions by Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA